Sound taxation? On the use of self-declared value

In the 16th century, foreign ships passing through the Sound had to pay ad valorem taxes, known as the Sound Dues. To give skippers an incentive to declare the true value of their cargo, the Danish Crown reserved the right to purchase it at the declared value. We show that it is an equilibrium for the authorities to confiscate the cargo with some fixed probability independent of the declared value. This does not induce truth-telling, but does generate the desired tax revenue. Other applications of this framework include the dissolution of partnerships, and the auditing of income tax returns.